A staircase baby is a descriptive term (used among black women) to define a child that was conceived while the parents engaged in sex/intercourse on a staircase. The term is most often associated with teenage Blacks who live in "projects". The Staircase baby term is not exclusive to project stairways. The term applies to any child that is conceived on a staircase (anywhere, anytime).
She kept sneaking out of the apartment to meet him, now she got a staircase baby.